It is known that function bkde2D (package "KernSmooth") returns a matrix of density estimates over the mesh induced by x1 and x2. In Details it is written that "... heights of the kernel, scaled by the bandwidths, at each datapoint are summed. This sum, after a normalization, is the corresponding fhat value in the output". There are several questions: 1) How to calculate amount (sum) of datapoints from this fhat value? Is it a non-normalized matrix of fhat values? 2) Values in fhat matrix are greater than 1 sometimes, why? Values of density are normalized and hence must be less than 1, isn't it?
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